The Experts below are selected from a list of 288 Experts worldwide ranked by ideXlab platform

Cristian Oara - One of the best experts on this subject based on the ideXlab platform.

Vlad Ionescu - One of the best experts on this subject based on the ideXlab platform.

Martin Bohner - One of the best experts on this subject based on the ideXlab platform.

  • Risk aversion and risk vulnerability in the continuous and Discrete Case
    Decisions in Economics and Finance, 2012
    Co-Authors: Martin Bohner, Gregory M. Gelles
    Abstract:

    This paper discusses utility functions for money, where allowable money values are from an arbitrary nonempty closed subset of the real numbers. Thus, the classical Case, where this subset is a closed interval (bounded or not) of the real line, is included in the study. The Discrete Case, where this subset is the set of all integer numbers, is also included. In a sense, the Discrete Case (which has not been addressed in the literature thus far) is more suitable for real-world applications than the continuous Case. In this general setting, the concepts of risk aversion and risk premium are defined, an analogue of Pratt’s fundamental theorem is proved, and temperance, prudence, and risk vulnerability are examined.

  • Risk aversion and risk vulnerability in the continuous and Discrete Case A unified treatment with extensions
    Decisions in Economics and Finance, 2011
    Co-Authors: Martin Bohner, Gregory M. Gelles
    Abstract:

    This paper discusses utility functions for money, where allowable money values are from an arbitrary nonempty closed subset of the real numbers. Thus, the classical Case, where this subset is a closed interval (bounded or not) of the real line, is included in the study. The Discrete Case, where this subset is the set of all integer numbers, is also included. In a sense, the Discrete Case (which has not been addressed in the literature thus far) is more suitable for real-world applications than the con- tinuous Case. In this general setting, the concepts of risk aversion and risk premium are defined, an analogue of Pratt's fundamental theorem is proved, and temperance, prudence, and risk vulnerability are examined.

  • Asymptotic Behavior of Dynamic Equations on Time Scales
    Journal of Difference Equations and Applications, 2001
    Co-Authors: Martin Bohner, D.a Lutz
    Abstract:

    As a way to unify a discussion of many kinds of problems for equations in the contionous and Discrete Case(but also in order to reveal discrepancies between both Cases), a theory of "time scales" was proposed and developed by Sulbach and Hilger. In our paper we investigate the asymptoic behaviour of so-called dynamic equations on time scales, and sych dynamic equations are differentialequations in the continous Case and difference equations in the Discrete Case. We offer a perturbation result that leads to a time scales version of Levinson's Fundamental Lemma. Crucial are a dichotomy condition and a growth condition on the perturbation. Also, in the Case that Levinson's result cannot be applied immediately, we suggest several preliminary transformations that might lead to a situation where Levinson's lemma is applicable. Such tranformations have been suggested by Harris and Lutz in the continuous Case and by Benzaid and Lutz in the Discrete Case. Both those Cases are covered by our theory, plus Cases "in ...

  • sturm liouville eigenvalue problems on time scales
    Applied Mathematics and Computation, 1999
    Co-Authors: Ravi P Agarwal, Martin Bohner, Patricia J Y Wong
    Abstract:

    For Sturm-Liouville eigenvalue problems on time scales with separated boundary conditions we give an oscillation theorem and establish Rayleigh's principle. Our results not only unifly the corresponding theories for differential and difference equations, but are also new in the Discrete Case.

Etienne E. Kerre - One of the best experts on this subject based on the ideXlab platform.

  • On the construction of interval-valued fuzzy morphological operators
    Fuzzy Sets and Systems, 2011
    Co-Authors: Tom Mélange, Mike Nachtegael, Peter Sussner, Etienne E. Kerre
    Abstract:

    Classical fuzzy mathematical morphology is one of the extensions of original binary morphology to greyscale morphology. Recently, this theory was further extended to interval-valued fuzzy mathematical morphology by allowing uncertainty in the grey values of the image and the structuring element. In this paper, we investigate the construction of increasing interval-valued fuzzy operators from their binary counterparts and work this out in more detail for the morphological operators, which results in a nice theoretical link between binary and interval-valued fuzzy mathematical morphology. The investigation is done both in the general continuous and the practical Discrete Case. It will be seen that the characterization of the supremum in the Discrete Case leads to stronger relationships than in the continuous Case.

  • Decomposing and constructing fuzzy morphological operations over /spl alpha/-cuts: continuous and Discrete Case
    IEEE Transactions on Fuzzy Systems, 2000
    Co-Authors: Mike Nachtegael, Etienne E. Kerre
    Abstract:

    Fuzzy mathematical morphology is an extension of binary morphology to gray-scale morphology, using techniques from fuzzy set theory. In this paper, we will study the decomposition and construction of fuzzy morphological operations based on /spl alpha/-cuts. First, we will investigate the relationship between /spl alpha/-cuts of the fuzzy morphological operations and the corresponding binary operations. Next, we will review several ways to obtain fuzzy morphological operations starting from binary operations and /spl alpha/-cuts. The investigation is carried out in both the continuous and the Discrete Case. It is interesting to observe that several properties that do not hold in the continuous Case do hold in the Discrete Case. This is quite important since in practice we only work with Discrete objects.

Gregory M. Gelles - One of the best experts on this subject based on the ideXlab platform.

  • Risk aversion and risk vulnerability in the continuous and Discrete Case
    Decisions in Economics and Finance, 2012
    Co-Authors: Martin Bohner, Gregory M. Gelles
    Abstract:

    This paper discusses utility functions for money, where allowable money values are from an arbitrary nonempty closed subset of the real numbers. Thus, the classical Case, where this subset is a closed interval (bounded or not) of the real line, is included in the study. The Discrete Case, where this subset is the set of all integer numbers, is also included. In a sense, the Discrete Case (which has not been addressed in the literature thus far) is more suitable for real-world applications than the continuous Case. In this general setting, the concepts of risk aversion and risk premium are defined, an analogue of Pratt’s fundamental theorem is proved, and temperance, prudence, and risk vulnerability are examined.

  • Risk aversion and risk vulnerability in the continuous and Discrete Case A unified treatment with extensions
    Decisions in Economics and Finance, 2011
    Co-Authors: Martin Bohner, Gregory M. Gelles
    Abstract:

    This paper discusses utility functions for money, where allowable money values are from an arbitrary nonempty closed subset of the real numbers. Thus, the classical Case, where this subset is a closed interval (bounded or not) of the real line, is included in the study. The Discrete Case, where this subset is the set of all integer numbers, is also included. In a sense, the Discrete Case (which has not been addressed in the literature thus far) is more suitable for real-world applications than the con- tinuous Case. In this general setting, the concepts of risk aversion and risk premium are defined, an analogue of Pratt's fundamental theorem is proved, and temperance, prudence, and risk vulnerability are examined.